Zero-sum game for nonlinear multiagent systems with full-state constraints

This paper addresses the zero-sum game problem for strict-feedback nonlinear multiagent systems with full-state constraints. Specifically, this paper focuses on the zero-sum game scenario, wherein multiple agents aim to optimize the control strategies while considering the conflicting objectives of their opponents. To handle the full-state constraints, a one-to-one nonlinear mapping technique is employed to convert the original strict-feedback system into a more manageable pure-feedback system without state constraints. In order to find a Nash equilibrium for virtual control signals and external disturbances, a simplified reinforcement learning algorithm is proposed, which tackles the challenges posed by solving the Hamilton-Jacobi-Isaacs equation. Unlike the existing H infinity$$ {H}_{\infty } $$ optimal control strategies that deal with matching conditions, the H infinity$$ {H}_{\infty } $$ optimal control strategy for strict-feedback nonlinear systems needs to address the computational complexity issue arising from the repeated derivation of the virtual controller. To overcome the high-order virtual controller problem, an approach based on the dynamic surface technique is introduced. By incorporating an approximation term of the high-order virtual controller into the value function, the computational complexity challenge is effectively resolved. Based on the Lyapunov stability theorem, it is proved that all signals of the closed-loop systems are semi-global uniformly ultimately bounded and the tracking control performance can be guaranteed. Finally, simulation results are given to verify the effectiveness of the proposed control strategy.